If Super Mario Bros. and Super Mario Bros. 3 were both released for the NES, how was SMB3 so much more advanced? [closed]

For example, SMB3 has a lot more levels, better graphics, more powerups, among other things. How was this possible if they were released for the same system? Was SMB1 purposefully held back?

There are at least a few key observations that may answer your question:

1.) SMB1 was not "held back." In fact, it featured some really clever programming tricks to make use of its 256 kilobit cartridge. Rather than try to explain it all myself, I'll direct you to this really awesome question on the retrocomputing stack exchange giving a high level explanation on how streamlined the programming needed to be to fit so much into such a small amount of memory without wasting even a handful of tiles.

2.) As for why Super Mario Bros 3 managed to bypass or push past the previous games' limitations, a lot of the advancements were in the cartridges, not the system. Keep in mind the NES' cartridges were literally circuit boards, and those boards could be designed more efficiently, with more hardware, and with higher grade hardware. For an easy and intuitive example (though not applicable to SMB and SMB3) see the inclusion of batteries and additional storage in some games but not in others that allowed for games saves. Borrowing from Wikipedia for at least one obvious advantage 3 had over 1:

The Super Mario Bros. 3 cartridge uses Nintendo's custom MMC3 (memory management controller) ASIC to enhance the NES capabilities. The MMC3 chip allows for animated tiles, extra RAM for diagonal scrolling, and a scan line timer to split the screen. The game uses these functions to split the game screen into two portions, a playfield on the top and a status bar on the bottom, allowing the top portion to scroll as the character navigates the stage while the bottom portion remains static to display text and other information.

3.) There were three years between SMB1 and SMB3, and the entire time the team that developed SMB1 and 3 was creating other games and experimenting with new tech and game development ideas. Shigeru Miyamoto acted as lead for both SMB1 and SMB3, and between the two games he developed level expansions for SMB, two Zelda games, and Super Mario Bros 2 (Or, as it was known in Japan, Doki Doki Panic)